ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields
This addresses the challenge of realistic 3D shape deformation and matching for applications like animation and computer graphics, representing a novel hybrid approach rather than a paradigm shift.
The paper tackles the problem of unsupervised prediction of physically plausible interpolations between 3D articulated shapes and automatic dense correspondence estimation, achieving competitive or superior performance over state-of-the-art approaches in both tasks.
This work presents a unified framework for the unsupervised prediction of physically plausible interpolations between two 3D articulated shapes and the automatic estimation of dense correspondence between them. Interpolation is modelled as a diffeomorphic transformation using a smooth, time-varying flow field governed by Neural Ordinary Differential Equations (ODEs). This ensures topological consistency and non-intersecting trajectories while accommodating hard constraints, such as volume preservation, and soft constraints, \eg physical priors. Correspondence is recovered using an efficient Varifold formulation, that is effective on high-fidelity surfaces with differing parameterisations. By providing a simple skeleton for the source shape only, we impose physically motivated constraints on the deformation field and resolve symmetric ambiguities. This is achieved without relying on skinning weights or any prior knowledge of the skeleton's target pose configuration. Qualitative and quantitative results demonstrate competitive or superior performance over existing state-of-the-art approaches in both shape correspondence and interpolation tasks across standard datasets.